Quantum circuit design speeds up solving equations in any finite field
A Quantum Circuit for Gaussian Elimination
Emerging Technologies
Summary
Solving systems of equations is important for many tasks in science and engineering. The authors developed a new quantum circuit that can perform Gaussian elimination, a common method for solving equations, but now on any finite field, not just simple binary ones. Their approach avoids unnecessary extra computations and keeps the process efficient in terms of the key quantum operations needed. This advancement could help in applying quantum computing to a wider range of mathematical problems.
What this means in practice
- •For quantum hardware engineers: Integrate an efficient quantum circuit for Gaussian elimination applicable to various finite fields in hardware designs.
- •For cryptography developers: Use the quantum circuit to potentially accelerate cryptographic protocols that rely on linear algebra over general finite fields.
Authors
Hochang Lee, Kyung Chul Jeong, Panjin Kim
Abstract
A quantum circuit for Gaussian elimination is developed in this work. While previous quantum implementations of Gaussian elimination were restricted to $\mathrm{GF}(2)$, the proposed design is generalized to any finite field. Compared with previous works in $\mathrm{GF}(2)$, the developed circuit achieves garbage-free construction while retaining the best known asymptotic Toffoli depth up to logarithmic factors.